Multivariate Hensel Lemma for ultrametric fields

Abstract

The Multivariate Hensel Lemma for local rings is usually proved as a consequence of the Grothendieck version of Zariski's Main Theorem. This version deals with a more general situation that is a priori much more difficult. In this paper, we give a direct proof of the Multivariate Hensel Lemma for ultrametric fields, in the framework of constructive mathematics and without using~ZMT. In the framework of classical mathematics, our result entails the Lemma for rank-one valued fields.

arXiv commentIn this file you find the English version, 15 pages, starting on the page numbered E1. Then the French version (Lemme de Hensel multivarié pour les corps ultramétriques), 15 pages, begins on the page numbered F1